{"id":70661,"date":"2018-02-20T23:50:30","date_gmt":"2018-02-20T23:50:30","guid":{"rendered":"https:\/\/writemyessayfree.com\/let-r-be-the-region-in-the-first-quadrant-bounded-by-the-graph-of-fx-sqrt1e-x-the-line-x2-and-the-x-axis-how-do-you-use-the-trapezoidal-rule-with-n4-to-approx-the-area"},"modified":"2017-08-18T06:14:44","modified_gmt":"2017-08-18T06:14:44","slug":"let-r-be-the-region-in-the-first-quadrant-bounded-by-the-graph-of-fx-sqrt1e-x-the-line-x2-and-the-x-axis-how-do-you-use-the-trapezoidal-rule-with-n4-to-approx-the-area","status":"publish","type":"post","link":"https:\/\/www.benedictsol.com\/blogs\/let-r-be-the-region-in-the-first-quadrant-bounded-by-the-graph-of-fx-sqrt1e-x-the-line-x2-and-the-x-axis-how-do-you-use-the-trapezoidal-rule-with-n4-to-approx-the-area\/","title":{"rendered":"Let R be the region in the first quadrant bounded by the graph of ##f(x) =sqrt(1+e^-x), the line x=2 and the x-axis, how do you use the trapezoidal rule with n=4 to approx the area?"},"content":{"rendered":"<p>##int_0^2sqrt(1+e^-x)dx ~~ A_T=2.391##<\/p>\n<p>Given ##n=4## trapezoids to use, you can measure the width of each trapezoid needed to estimate the area. Divide the difference of your bounds by the number of trapezoids you have. <\/p>\n<p>##Deltax = (2-0)\/4## ##Deltax = 1\/2##<\/p>\n<p>The area in question ranges from## x = 0## (the y axis) to the line ##x = 2## and is bounded by the ##x## axis and the function. Starting at ##x = 0##, create a new trapezoid base by increments of ##Deltax##, which is ##1\/2##. Your can draw a picture based on that information.<\/p>\n<p>All you have to do now is find the area of each separate trapezoid drawn and total them. ##A_T =[(b_1 + b_2)\/2] * h##<\/p>\n<p>The trapezoids are sideways if you ever find yourself confused:<\/p>\n<p>##A~~ [f(0) + f(1\/2)]\/2*(1\/2) + [f(1\/2) + f(1)]\/2*(1\/2) + [f(1) + f(3\/2)]\/2*(1\/2) + [f(3\/2) + f(2)]\/2*(1\/2)##<\/p>\n<p>##A ~~ (1\/4)[ f(0) + 2*f(1\/2) + 2*f(1) + 2*f(3\/2) + f(2)]##<\/p>\n<p>##A~~2.391##<\/p>\n","protected":false},"excerpt":{"rendered":"<p>##int_0^2sqrt(1+e^-x)dx ~~ A_T=2.391## Given ##n=4## trapezoids to use, you can measure the width of each trapezoid needed to estimate the area. Divide the difference of your bounds by the number of trapezoids you have. ##Deltax = (2-0)\/4## ##Deltax = 1\/2## <a href=\"https:\/\/www.benedictsol.com\/blogs\/let-r-be-the-region-in-the-first-quadrant-bounded-by-the-graph-of-fx-sqrt1e-x-the-line-x2-and-the-x-axis-how-do-you-use-the-trapezoidal-rule-with-n4-to-approx-the-area\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-70661","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/70661","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=70661"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/70661\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=70661"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=70661"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=70661"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}